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Spurious correlation #13,385 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of movies Dwayne Johnson appeared in and the second variable is Global revenue generated by McDonald's.  The chart goes from 2005 to 2022, and the two variables track closely in value over that time. Small Image
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Data details

The number of movies Dwayne Johnson appeared in
Source: The Movie DB
Additional Info: The Rundown (2003); Southland Tales (2006); Walking Tall (2004); Tooth Fairy (2010); Doom (2005); The Scorpion King (2002); Gridiron Gang (2006); The Game Plan (2007); Race to Witch Mountain (2009); Faster (2010); WWE Survivor Series 2001 (2001); Planet 51 (2009); Journey 2: The Mysterious Island (2012); The Rock: The Epic Journey of Dwayne Johnson (2012); WWE WrestleMania XXVIII (2012); WWE Royal Rumble 2002 (2002); WWE Royal Rumble 1999 (1999); Snitch (2013); WWE WrestleMania 29 (2013); Hercules (2014); WWE Elimination Chamber 2013 (2013); WWE Unforgiven 2000 (2000); WWE WrestleMania X-Seven (2001); WWE Unforgiven 1999 (1999); WWE WrestleMania XV (1999); WWE Backlash 2000 (2000); WWE Rebellion 1999 (1999); WWE SummerSlam 2000 (2000); WWF Fully Loaded 2000 (2000); WWE Insurrextion 2000 (2000); WWE Vengeance 2002 (2002); WWE Global Warning (2002); WWE Backlash 2003 (2003); WWE No Way Out 2003 (2003); WWF: The Rock - The People's Champ (2000); The Rock - Just Bring It! (2002); WWF: The Rock - Know Your Role (1998); WWF: Funniest Moments (2002); Rampage (2018); WWE: Attitude Era: Vol. 2 (2014); Jungle Cruise (2021); WWE Collection Volume 2: Know Your Role (2015); Central Intelligence (2016); Baywatch (2017); San Andreas (2015); Jumanji: Welcome to the Jungle (2017); WWE: The Rock: The Most Electrifying Man in Sports Entertainment - Vol. 3 (2011); WWE: The Rock: The Most Electrifying Man in Sports Entertainment (2008); WWE: The Rock: The Most Electrifying Man in Sports Entertainment - Vol. 2 (2010); G.I. Joe: Retaliation (2013); Skyscraper (2018); Fast & Furious Presents: Hobbs & Shaw (2019); Black Adam (2022); Rock and a Hard Place (2017); Jumanji: The Next Level (2019); Red Notice (2021); WWF: Best of Raw - Vol. 1 (1998); Mickey’s 90th Spectacular (2018); The Rock's Most Electrifying Matches (2020); WWE: The Attitude Era (2012); WWE Halftime Heat (1999); DC League of Super-Pets (2022); WWE: Monday Night War Vol. 2: Know Your Role (2015); Black Adam: Saviour or Destroyer? (2022); WWE: Greatest Wrestling Stars of the '90s (2009); WWE SummerSlam 2002 (2002); Pain & Gain (2013); Empire State (2013); WWE No Way Out 2001 (2001); WWE Survivor Series 1999 (1999); WWE Backlash: In Your House (1999); WWE No Mercy 2000 (2000); WWE Rebellion 2000 (2000); WWE Judgment Day 2000 (2000); WWE SummerSlam 2001 (2001); WWE Rebellion 2001 (2001); WWE Vengeance 2001 (2001); WWE: The Rock vs John Cena: Once in a Lifetime (2012); Brock Lesnar: Best of the Beast (2014); Moana (2016); Gone Fishing (2017); WWF: Best of Raw - Vol. 1&2 (2001); WWF: Chris Jericho - Break Down the Walls (2000); My Way: The Life and Legacy of Pat Patterson (2021); The Mummy Returns (2001); Get Smart (2008); Fast & Furious 6 (2013); WWE Wrestlemania XIX (2003); WWE Royal Rumble 2000 (2000); WWE WrestleMania 2000 (2000); WWE Unforgiven 2001 (2001); WWE SummerSlam 1998 (1998); WWE Over the Edge (1999); WWE Armageddon 2000 (2000); WWF: Mick Foley - Hard Knocks & Cheap Pops (2001); WWF: Undertaker The Phenom (1998); WWE: The Videos Ramped Up Vol. 1 (2002); The Fate of the Furious (2017); WWE: Top 50 Superstars of All Time (2010); WWE: Triple H: Thy Kingdom Come (2013); WWE: Best Pay-Per-View Matches of 2013 (2013); WWE: Monday Night War Vol. 1: Shots Fired (2015); Voice of the Islands (2017); WWE: Greatest Stars Of The 90's (2013); For All Mankind - The Life and Career of Mick Foley (2013); WWE WrestleMania XXVII (2011); Summer Game Fest 2022 (2022); Angle (2023); WWE Rivals: Steve Austin vs. The Rock (2022); WWE Survivor Series 2011 (2011); WWE Judgment Day: In Your House (1998); WWE Survivor Series 1998 (1998); WWE D-Generation X: In Your House (1997); WWE St. Valentine's Day Massacre: In Your House (1999); WWE Rock Bottom: In Your House (1998); WWE Fully Loaded 1999 (1999); WWE No Way Out 2000 (2000); WWE King of the Ring 2000 (2000); The Sheik (2014); Escape from Calypso Island (2016); Biography: “Stone Cold” Steve Austin (2021); Be Cool (2005); WWE King of the Ring 1998 (1998); WWE Capital Carnage (1998); WWE King of the Ring 1999 (1999); WWE SummerSlam 1999 (1999); WWE No Mercy 2001 (2001); WWE No Way Out 2002 (2002); WWF: Stone Cold Steve Austin: What? (2002); WWE's Biggest Knuckleheads (2011); WWE: 30 Years of SummerSlam (2018); WWE: Raw 10th Anniversary (2003); The Top 100 Moments In Raw History (2012); Meeting Stone Cold (2021); WWE Tagged Classics: Austin 3:16 Uncensored / Three Faces Of Foley / Chris Jericho: Break Down The Walls / Kurt Angle: Its True (2012); Biography: Kurt Angle (2022); USIDent TV: Surveilling the Southland (2008); WWE: 50 Greatest Finishing Moves in WWE History (2012); WWE: Triple H - That Damn Good (2002); Fighting with My Family (2019); WWE: The Best of King of the Ring (2011); Kurt Angle: The Essential Collection (2017); Rock Bottom Riser (2021); Never Forget: WWE Returns After 9/11 (2021); WWE Royal Rumble 1998 (1998); WWE In Your House 14: Revenge of the Taker (1997); WWE Fully Loaded: In Your House (1998); WWE Armageddon 1999 (1999); WWE: Greatest Superstars of the 21st Century (2011); WWE: John Cena's Greatest Rivalries (2014); Stone Cold Steve Austin: The Bottom Line on the Most Popular Superstar of All Time (2011); Randy Orton: The Evolution of a Predator (2011); The True Story of WrestleMania (2011); WWE: Brock Lesnar: Here Comes the Pain (2003); Superfan: The Story of Vladimir (2023); The Other Guys (2010); WWE Royal Rumble 2013 (2013); WWE Survivor Series 1996 (1996); Furious 7 (2015); WWE: The Best of Raw - After the Show (2014); WWE: The True Story of The Royal Rumble (2016); WWE: Best of the 2000's (2017); WWE Wrestlemania X8 (2002); WWE In Your House 13: Final Four (1997); Elvis: Viva Las Vegas (2008); WWE: Best Pay-Per-View Matches 2012 (2012); WWE: Hell in a Cell - The Greatest Hell in a Cell Matches of All Time (2008); WWE WrestleMania XIV (1998); WWE In Your House 15: A Cold Day in Hell (1997); WWE: The Best of Raw 15th Anniversary (2007); WWE: The Ladder Match (2007); 1997: Dawn of the Attitude (2017); Millennials: The Musical (2016); Iron and Beyond (2002); Operation Filmmaker (2008); Why Did I Get Married Too? (2010); WWE: 150 Best Pay-Per-View Matches, Vol 2 (2014); Starrcast V: The Roast of Ric Flair (2022); Hart & Soul - The Hart Family Anthology (2010); Fast Five (2011); WWE Over the Edge: In Your House (1998); WWE Survivor Series 1997 (1997); WWE: The Legacy of Stone Cold Steve Austin (2008); WWE: The Best of Raw & SmackDown 2012 (2013); Hollywood Hulk Hogan: Hulk Still Rules (2002); WWE In Your House 12: It's Time (1996); WWE Breakdown: In Your House (1998); WWE: Wrestlemania Recall (2005); Breaking the Code: Behind the Walls of Chris Jericho (2010); WWE: Tombstone - The History of the Undertaker (2005); The Ladder Match 2: Crash & Burn (2011); WWE RAW 1000 (2012); WWE Survivor Series 2000 (2000); The Road is Jericho: Epic Stories and Rare Matches from Y2J (2015); WWE: 30 Years of Survivor Series (2017); Beyond the Mat (1999); Owen Hart of Gold (2015); WWE: The Best of the Intercontinental Championship (2005); WWE No Mercy 1999 (1999); WWE: WrestleMania Monday (2017); WWE No Way Out of Texas: In Your House (1998); The Words That Built America (2017); The History of WWE: 50 Years of Sports Entertainment (2013); WWE Mayhem in Manchester (1998); 30 Rock: A One-Time Special (2020); WWE WrestleMania 13 (1997); WWE Unforgiven: In Your House (1998); WWE: The History Of The World Heavyweight Championship (2009); WWE Badd Blood: In Your House (1997); WWE: The History Of The Intercontinental Championship (2008); WWE: Mick Foley's Greatest Hits & Misses - A Life in Wrestling (2004); The History of The WWE Hardcore Championship (2016); WWE: The History Of The WWE Championship (2006); Free Guy (2021); WWE WrestleMania 31 (2015); WWE Royal Rumble 2001 (2001); Longshot (2001); Bret Hart: The Dungeon Collection (2013); Trish & Lita – Best Friends, Better Rivals (2019); WWE WrestleMania 32 (2016); WWE: The Big Show - A Giant's World (2011); WWE: Hulk Hogan: The Ultimate Anthology (2006); WWE: Falls Count Anywhere: The Greatest Street Fights and Other Out of Control Matches (2012); WWE: The Best Of In Your House (2013); WWE: OMG! The Top 50 Incidents in WWE History (2011); WWE King of the Ring 2002 (2002); Straight Outta Dudleyville: The Legacy of the Dudley Boyz (2016); Once Upon a Studio (2023); WWE Royal Rumble 1997 (1997); WWE: The Best of SmackDown - 10th Anniversary, 1999-2009 (2012); Jem and the Holograms (2015); Fast X (2023); WWE: Best of WWE at Madison Square Garden (2013); You Again (2010); WWE Royal Rumble 2015 (2015); WWE WrestleMania XX (2004); WWE: 150 Best Pay-Per-View Matches, Vol 1 (2014); Reno 911!: Miami (2007); WWE WrestleMania XXX (2014)

See what else correlates with The number of movies Dwayne Johnson appeared in

Global revenue generated by McDonald's
Source: Statista
See what else correlates with Global revenue generated by McDonald's

Correlation r = 0.8383785 (Pearson correlation coefficient)
Correlation is a measure of how much the variables move together. If it is 0.99, when one goes up the other goes up. If it is 0.02, the connection is very weak or non-existent. If it is -0.99, then when one goes up the other goes down. If it is 1.00, you probably messed up your correlation function.

r2 = 0.7028785 (Coefficient of determination)
This means 70.3% of the change in the one variable (i.e., Global revenue generated by McDonald's) is predictable based on the change in the other (i.e., The number of movies Dwayne Johnson appeared in) over the 18 years from 2005 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.4E-5. 0.0000139128368471307170000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

But I am a p-villain. I absolutely did not test only one pair of variables one time. I correlated hundreds of millions of pairs of variables. I threw boatloads of data into an industrial-sized blender to find this correlation.

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.84 in 0.0014% of random cases. Said differently, if you correlated 71,876 random variables You don't actually need 71 thousand variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

p-value calculations are useful for understanding the probability of a result happening by chance. They are most useful when used to highlight the risk of a fluke outcome. For example, if you calculate a p-value of 0.30, the risk that the result is a fluke is high. It is good to know that! But there are lots of ways to get a p-value of less than 0.01, as evidenced by this project.

In this particular case, the values are so extreme as to be meaningless. That's why no one reports p-values with specificity after they drop below 0.01.

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 17 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 17 because we have two variables measured over a period of 18 years. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to the number of years minus one.
you would randomly expect to find a correlation as strong as this one.

[ 0.61, 0.94 ] 95% correlation confidence interval (using the Fisher z-transformation)
The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!


All values for the years included above: If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.
200520062007200820092010201120122013201420152016201720182019202020212022
The number of movies Dwayne Johnson appeared in (Movie appearances)54484913121791081244287
Global revenue generated by McDonald's (Billion US Dollars)19.1220.922.7923.5222.7524.0827.0127.5728.1127.4425.4124.6222.8221.0321.0819.2123.2223.18




Why this works

  1. Data dredging: I have 25,237 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 636,906,169 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
  2. Lack of causal connection: There is probably Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
    no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
  3. Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
    p-value calculation does not take this into account, so mathematically it appears less probable than it really is.
  4. Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
    Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.
  5. Outlandish outliers: There are "outliers" in this data. In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

    For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

    (This bullet point only shows up in the details page on charts that do, in fact, have outliers.)
    They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.




Try it yourself

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. Step 1: Download and install Python on your computer.

Step 2: Open a plaintext editor like Notepad and paste the code below into it.

Step 3: Save the file as "calculate_correlation.py" in a place you will remember, like your desktop. Copy the file location to your clipboard. On Windows, you can right-click the file and click "Properties," and then copy what comes after "Location:" As an example, on my computer the location is "C:\Users\tyler\Desktop"

Step 4: Open a command line window. For example, by pressing start and typing "cmd" and them pressing enter.

Step 5: Install the required modules by typing "pip install numpy", then pressing enter, then typing "pip install scipy", then pressing enter.

Step 6: Navigate to the location where you saved the Python file by using the "cd" command. For example, I would type "cd C:\Users\tyler\Desktop" and push enter.

Step 7: Run the Python script by typing "python calculate_correlation.py"

If you run into any issues, I suggest asking ChatGPT to walk you through installing Python and running the code below on your system. Try this question:

"Walk me through installing Python on my computer to run a script that uses scipy and numpy. Go step-by-step and ask me to confirm before moving on. Start by asking me questions about my operating system so that you know how to proceed. Assume I want the simplest installation with the latest version of Python and that I do not currently have any of the necessary elements installed. Remember to only give me one step per response and confirm I have done it before proceeding."


# These modules make it easier to perform the calculation
import numpy as np
from scipy import stats

# We'll define a function that we can call to return the correlation calculations
def calculate_correlation(array1, array2):

    # Calculate Pearson correlation coefficient and p-value
    correlation, p_value = stats.pearsonr(array1, array2)

    # Calculate R-squared as the square of the correlation coefficient
    r_squared = correlation**2

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([5,4,4,8,4,9,13,12,17,9,10,8,12,4,4,2,8,7,])
array_2 = np.array([19.12,20.9,22.79,23.52,22.75,24.08,27.01,27.57,28.11,27.44,25.41,24.62,22.82,21.03,21.08,19.21,23.22,23.18,])
array_1_name = "The number of movies Dwayne Johnson appeared in"
array_2_name = "Global revenue generated by McDonald's"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)



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Correlation ID: 13385 · Black Variable ID: 26563 · Red Variable ID: 432
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